This month marks the 100th anniversary of the General Theory of Relativity, the most beautiful theory in the history of science, and in its honor we should take a moment to celebrate the visualized “thought experiments” that were the navigation lights guiding Albert Einstein to his brilliant creation. Einstein relished what he called Gedankenexperimente, ideas that he twirled around in his head rather than in a lab. That’s what teachers call daydreaming, but if you’re Einstein you get to call them Gedankenexperimente.
As these thought experiments remind us, creativity is based on imagination. If we hope to inspire kids to love science, we need to do more than drill them in math and memorized formulas. We should stimulate their minds’ eyes as well. Even let them daydream.
Einstein’s first great thought experiment came when he was about 16. He had run away from his school in Germany, which he hated because it emphasized rote learning rather than visual imagination, and enrolled in a Swiss village school based on the educational philosophy of Johann Heinrich Pestalozzi, who believed in encouraging students to visualize concepts. While there, Einstein tried to picture what it would be like to travel so fast that you caught up with a light beam. If he rode alongside it, he later wrote, “I should observe such a beam of light as an electromagnetic field at rest.” In other words, the wave would seem stationary. But this was not possible according to Maxwell’s equations, which describe the motion and oscillation of electromagnetic fields.
The conflict between his thought experiment and Maxwell’s equations caused Einstein “psychic tension,” he later recalled, and he wandered around nervously, his palms sweating. Some of us can recall what made our palms sweaty as teenagers, and those thoughts didn’t involve Maxwell’s equations. But that’s because we were probably performing less elevated thought experiments.
By the early 1900s, a variety of experiments showed that light traveled at a constant speed, irrespective of the observer’s motion relative to the light source. The physics community was puzzled by this, just as Einstein was still puzzled by his attempts to imagine riding alongside a light beam. So, in 1905, he performed some new thought experiments.
He was then working at the Swiss patent office. Every day, he would attempt to visualize how an invention and its underlying theoretical premises would play out in reality. Among his tasks was examining applications for devices to synchronize distant clocks. The Swiss (being Swiss) had a passion for making sure that clocks throughout the country were precisely in sync. As the Harvard historian of science Peter Galison has found, more than two dozen patents were issued from Einstein’s office between 1901 and 1904 for devices that used electromagnetic signals such as radio and light to synchronize clocks.
What Einstein was able to visualize was that if you sent a light signal from the clocks the instant they struck the hour, a person traveling superfast toward one of the clocks would have a different view of whether they were in sync than someone traveling superfast in the other direction.
He later explained this idea with another thought experiment. Suppose lightning bolts strike a train track at two distant places. Imagine that there’s a man standing on the embankment midpoint between the two strikes. If the light from each bolt reaches him at the same instant, he will say the strikes were simultaneous. Now imagine that there’s a woman in the midpoint of the train just passing him. If the train is moving forward superfast, by the time the light waves arrive she will be slightly closer to the lightning bolt in front. She will declare that it happened first.
“Events that are simultaneous with reference to the embankment are not simultaneous with respect to the train,” wrote Einstein. Here’s the fun part: There is no reason to decree that the man is right and the woman wrong, because there’s no reason to assume that the embankment is “at rest” and the train “in motion.” The man, woman, train, Earth, solar system, galaxy, etc., are all in motion relative to one another, and none of them can claim the privileged status of being at absolute rest. So there is no “real” or “right” answer. What is “simultaneous” is relative, depending on your state of motion.
That means time is relative. If you travel near the speed of light, time slows down. Don’t feel bad if you can’t grasp this right away. It was another four years before Einstein was able to get a job at a university teaching physics.
This relativity of space and time became known as the Special Theory, because it applied only to a special case: an observer moving at a constant velocity. It’s harder to make the more general case that the same principles apply to a person who is accelerating or turning or rotating. It would take Einstein a decade more to come up with a General Theory that applied to all forms of motion.
Once again, his path was lit by a thought experiment. “I was sitting in a chair in the patent office at Bern when all of a sudden a thought occurred to me,” he recalled. “If a person falls freely, he will not feel his own weight.” He later called it “the happiest thought in my life.”
If the man were in a falling chamber with no windows, Einstein realized, he would not know he was falling (at least until he crashed into the ground). Instead, he might think he was in a chamber in outer space where there was no gravity. He would feel weightless, and if he pulled an object from his pocket and let it go, it would float freely alongside him.
Then Einstein flipped the script. Imagine that the man was floating in an enclosed chamber deep in outer space where no gravity was perceptible. Now suppose a hook is attached atop this chamber and it is pulled upward at an accelerated rate. What would the man feel? His feet would be pressed to the floor. If he pulled something out of his pocket and let it go, it would fall toward the floor at an accelerated rate. “The man in the chamber will thus come to the conclusion that he and the chamber are in a gravitational field,” Einstein wrote.
The effects produced by gravity and the effects produced by acceleration are equivalent, Einstein postulated. Thus they must have the same cause. “The effects we ascribe to gravity and the effects we ascribe to acceleration are both produced by one and the same structure,” he declared.
In his Special Theory, Einstein had shown that space and time were not independent, but instead formed a fabric of “space-time.” Now, with his general version of the theory, which became known as the General Theory of Relativity, this fabric of space-time became not merely a container for objects. Instead, it had its own two-way dynamics: moving objects would curve the fabric, and the curves of the fabric would influence how objects moved.
This can be visualized through yet another thought experiment: Imagine rolling a bowling ball onto a trampoline. It will curve the fabric. Then put some billiard balls onto it. They will gradually roll toward the bowling ball — not because the bowling ball exerts some mysterious attraction at a distance, but instead because it has curved the fabric of the trampoline. Einstein was able to visualize this happening to the four-dimensional fabric of space and time. Admittedly, that’s a bit hard for us to imagine, but that’s why he was Einstein and we aren’t.
On four consecutive Thursdays in November 1915, Einstein laid out his General Theory to the Prussian Academy of Sciences in Berlin. In his final lecture, on Nov. 25, he produced the equations that describe the gravitational-inertial field. Einstein’s final equations used the condensed notations of tensors to compress sprawling complexities into squiggly symbols and subscripts, making them compact enough to be printed on T-shirts for physics geeks. In one of its variations it can be written as: Rμν – ½ Rgμν = 8 π G Tμν
The left side of the equation describes how objects warp and curve the geometry of space-time. The right side describes how this warped and curved field dictates the way objects move. As the physicist John Wheeler put it: “Matter tells space-time how to curve, and curved space tells matter how to move.”
One consequence of the equivalence between gravity and acceleration is that gravity should bend a light beam. Einstein showed this through yet another thought experiment. Imagine a chamber that is being accelerated upward. A laser beam comes in through a pinhole on one wall. When it hits the opposite wall, it will be at a spot closer to the floor, because the chamber has moved upward. If you could track it, the trajectory would seem curved, because the upward motion is accelerating. According to the equivalence principle, the effect of gravity is the same as that of acceleration, so light should curve as it goes through a gravitational field.
It was almost four years before scientists were able to conduct a convincing test of the theory. During a May 1919 eclipse of the sun, a team led by the British astronomer Arthur Eddington was able to measure how light coming from a star was bent as it passed through the gravitational field close to the sun. The results confirmed Einstein’s theory.
When Einstein got a telegram informing him, he showed it to a graduate student. What, she asked, would Einstein have felt if the observations had disproved his theory? “Then I would have been sorry for the dear Lord,” he replied. “The theory is correct.” Newspapers knew how to write great headlines back then, and the six-deck one in The New York Times became a classic: “LIGHTS ALL ASKEW IN THE HEAVENS / Men of Science More or Less Agog Over Results of Eclipse Observations / Einstein Theory Triumphs / Stars Not Where They Seemed or Were Calculated to be, but Nobody Need Worry.”
Years later, when his younger son, Eduard, asked why he was so famous, Einstein replied by using another simple thought experiment to describe his insight that gravity was the curving of the fabric of space-time. “When a blind beetle crawls over the surface of a curved branch, it doesn’t notice that the track it has covered is indeed curved,” he said. “I was lucky enough to notice what the beetle didn’t notice.”
In fact, Einstein did more than just notice what the blind beetle couldn’t see. He was able to imagine it by conjuring up thought experiments. That ability to visualize the unseen has always been the key to creative genius. As Einstein later put it, “Imagination is more important than knowledge.”
Walter Isaacson, the C.E.O. of the Aspen Institute, is the author of The Innovators and biographies of Einstein, Steve Jobs, Benjamin Franklin and Henry Kissinger.